Abstract

A piezoelectric detector with a cylindrical shape is investigated for photoacoustic section imaging. Images are acquired by rotating a sample in front of the cylindrical detector. With its length exceeding the size of the imaging object, it works as an integrating sensor and therefore allows reconstructing section images with the inverse Radon transform. Prior to the reconstruction the Abel transform is applied to the measured signals to improve the accuracy of the image. A resolution of about 100 µm within a section and of 500 µm between sections is obtained. Additionally, a series of images of a zebra fish is shown.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. H. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum.77(4), 041101 (2006).
    [CrossRef]
  2. R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging2(2), 113–123 (2003).
    [CrossRef] [PubMed]
  3. X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003).
    [CrossRef] [PubMed]
  4. R. Ma, A. Taruttis, V. Ntziachristos, and D. Razansky, “Multispectral optoacoustic tomography (MSOT) scanner for whole-body small animal imaging,” Opt. Express17(24), 21414–21426 (2009).
    [CrossRef] [PubMed]
  5. Z. Xu, Q. Zhu, and L. V. Wang, “In vivo photoacoustic tomography of mouse cerebral edema induced by cold injury,” J. Biomed. Opt.16(6), 066020 (2011).
    [CrossRef] [PubMed]
  6. R. G. M. Kolkman, W. Steenbergen, and T. G. van Leeuwen, “In vivo photoacoustic imaging of blood vessels with a pulsed laser diode,” Lasers Med. Sci.21(3), 134–139 (2006).
    [CrossRef] [PubMed]
  7. J. Laufer, J. O. Cleary, E. Z. Zhang, M. F. Lythgoe, and P. C. Beard, “Photoacoustic imaging of vascular networks in transgenic mice,” Proc. SPIE7564, 75641A, 75641A-5 (2010).
    [CrossRef]
  8. M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
    [CrossRef] [PubMed]
  9. S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
    [CrossRef] [PubMed]
  10. S. Manohar, A. Kharine, J. C. van Hespen, W. Steenbergen, and T. G. van Leeuwen, “The Twente Photoacoustic Mammoscope: system overview and performance,” Phys. Med. Biol.50(11), 2543–2557 (2005).
    [CrossRef] [PubMed]
  11. M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
    [CrossRef]
  12. U. Oberheide, I. Bruder, H. Welling, W. Ertmer, and H. Lubatschowski, “Optoacoustic imaging for optimization of laser cyclophotocoagulation,” J. Biomed. Opt.8(2), 281–287 (2003).
    [CrossRef] [PubMed]
  13. M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl.20(5), 1663–1673 (2004).
    [CrossRef]
  14. P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography using integrating detectors,” Proc. SPIE5864, 586403, 586403-12 (2005).
    [CrossRef]
  15. D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
    [CrossRef]
  16. P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control52(9), 1577–1583 (2005).
    [CrossRef] [PubMed]
  17. G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Photoacoustic tomography with integrating area and line detectors,” in Photoacoustic Imaging and Spectroscopy, L. V. Wang, ed. (CRC Press, Boca Raton, FL, 2009), pp. 251–263.
  18. P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Probl.23(6), S65–S80 (2007).
    [CrossRef]
  19. D. Xiang, N. N. Hsu, and G. V. Blessing, “The design, construction and application of a large aperture lens-less line-focus PVDF transducer,” Ultrasonics34(6), 641–647 (1996).
    [CrossRef]
  20. A. Oraevsky and A. Karabutov, “Ultimate sensitivity of time-resolved opto-acoustic detection,” Proc. SPIE3916, 228–239 (2000).
    [CrossRef]
  21. A. Rosenthal, V. Ntziachristos, and D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys.38(7), 4285–4295 (2011).
    [CrossRef] [PubMed]
  22. M. Haltmeier and G. Zangerl, “Spatial resolution in photoacoustic tomography: effects of detector size and detector bandwidth,” Inverse Probl.26(12), 125002 (2010).
    [CrossRef]
  23. M. H. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056605 (2003).
    [CrossRef] [PubMed]

2011

Z. Xu, Q. Zhu, and L. V. Wang, “In vivo photoacoustic tomography of mouse cerebral edema induced by cold injury,” J. Biomed. Opt.16(6), 066020 (2011).
[CrossRef] [PubMed]

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

A. Rosenthal, V. Ntziachristos, and D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys.38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

2010

M. Haltmeier and G. Zangerl, “Spatial resolution in photoacoustic tomography: effects of detector size and detector bandwidth,” Inverse Probl.26(12), 125002 (2010).
[CrossRef]

J. Laufer, J. O. Cleary, E. Z. Zhang, M. F. Lythgoe, and P. C. Beard, “Photoacoustic imaging of vascular networks in transgenic mice,” Proc. SPIE7564, 75641A, 75641A-5 (2010).
[CrossRef]

M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
[CrossRef] [PubMed]

2009

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
[CrossRef]

R. Ma, A. Taruttis, V. Ntziachristos, and D. Razansky, “Multispectral optoacoustic tomography (MSOT) scanner for whole-body small animal imaging,” Opt. Express17(24), 21414–21426 (2009).
[CrossRef] [PubMed]

2007

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Probl.23(6), S65–S80 (2007).
[CrossRef]

2006

R. G. M. Kolkman, W. Steenbergen, and T. G. van Leeuwen, “In vivo photoacoustic imaging of blood vessels with a pulsed laser diode,” Lasers Med. Sci.21(3), 134–139 (2006).
[CrossRef] [PubMed]

M. H. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum.77(4), 041101 (2006).
[CrossRef]

2005

S. Manohar, A. Kharine, J. C. van Hespen, W. Steenbergen, and T. G. van Leeuwen, “The Twente Photoacoustic Mammoscope: system overview and performance,” Phys. Med. Biol.50(11), 2543–2557 (2005).
[CrossRef] [PubMed]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography using integrating detectors,” Proc. SPIE5864, 586403, 586403-12 (2005).
[CrossRef]

2004

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl.20(5), 1663–1673 (2004).
[CrossRef]

2003

M. H. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056605 (2003).
[CrossRef] [PubMed]

U. Oberheide, I. Bruder, H. Welling, W. Ertmer, and H. Lubatschowski, “Optoacoustic imaging for optimization of laser cyclophotocoagulation,” J. Biomed. Opt.8(2), 281–287 (2003).
[CrossRef] [PubMed]

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging2(2), 113–123 (2003).
[CrossRef] [PubMed]

X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003).
[CrossRef] [PubMed]

2000

A. Oraevsky and A. Karabutov, “Ultimate sensitivity of time-resolved opto-acoustic detection,” Proc. SPIE3916, 228–239 (2000).
[CrossRef]

1996

D. Xiang, N. N. Hsu, and G. V. Blessing, “The design, construction and application of a large aperture lens-less line-focus PVDF transducer,” Ultrasonics34(6), 641–647 (1996).
[CrossRef]

Bauer-Marschallinger, J.

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Probl.23(6), S65–S80 (2007).
[CrossRef]

Beard, P. C.

J. Laufer, J. O. Cleary, E. Z. Zhang, M. F. Lythgoe, and P. C. Beard, “Photoacoustic imaging of vascular networks in transgenic mice,” Proc. SPIE7564, 75641A, 75641A-5 (2010).
[CrossRef]

Blessing, G. V.

D. Xiang, N. N. Hsu, and G. V. Blessing, “The design, construction and application of a large aperture lens-less line-focus PVDF transducer,” Ultrasonics34(6), 641–647 (1996).
[CrossRef]

Brecht, H. P.

M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
[CrossRef] [PubMed]

Bruder, I.

U. Oberheide, I. Bruder, H. Welling, W. Ertmer, and H. Lubatschowski, “Optoacoustic imaging for optimization of laser cyclophotocoagulation,” J. Biomed. Opt.8(2), 281–287 (2003).
[CrossRef] [PubMed]

Burgholzer, P.

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Probl.23(6), S65–S80 (2007).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography using integrating detectors,” Proc. SPIE5864, 586403, 586403-12 (2005).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl.20(5), 1663–1673 (2004).
[CrossRef]

Cleary, J. O.

J. Laufer, J. O. Cleary, E. Z. Zhang, M. F. Lythgoe, and P. C. Beard, “Photoacoustic imaging of vascular networks in transgenic mice,” Proc. SPIE7564, 75641A, 75641A-5 (2010).
[CrossRef]

Conjusteau, A.

M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
[CrossRef] [PubMed]

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

Distel, M.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
[CrossRef]

Ermilov, S. A.

M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
[CrossRef] [PubMed]

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

Ertmer, W.

U. Oberheide, I. Bruder, H. Welling, W. Ertmer, and H. Lubatschowski, “Optoacoustic imaging for optimization of laser cyclophotocoagulation,” J. Biomed. Opt.8(2), 281–287 (2003).
[CrossRef] [PubMed]

Fronheiser, M. P.

M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
[CrossRef] [PubMed]

Grün, H.

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Probl.23(6), S65–S80 (2007).
[CrossRef]

Haltmeier, M.

M. Haltmeier and G. Zangerl, “Spatial resolution in photoacoustic tomography: effects of detector size and detector bandwidth,” Inverse Probl.26(12), 125002 (2010).
[CrossRef]

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Probl.23(6), S65–S80 (2007).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography using integrating detectors,” Proc. SPIE5864, 586403, 586403-12 (2005).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl.20(5), 1663–1673 (2004).
[CrossRef]

Heijblom, M.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

Hofer, C.

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography using integrating detectors,” Proc. SPIE5864, 586403, 586403-12 (2005).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

Hsu, N. N.

D. Xiang, N. N. Hsu, and G. V. Blessing, “The design, construction and application of a large aperture lens-less line-focus PVDF transducer,” Ultrasonics34(6), 641–647 (1996).
[CrossRef]

Karabutov, A.

A. Oraevsky and A. Karabutov, “Ultimate sensitivity of time-resolved opto-acoustic detection,” Proc. SPIE3916, 228–239 (2000).
[CrossRef]

Khamapirad, T.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

Kharine, A.

S. Manohar, A. Kharine, J. C. van Hespen, W. Steenbergen, and T. G. van Leeuwen, “The Twente Photoacoustic Mammoscope: system overview and performance,” Phys. Med. Biol.50(11), 2543–2557 (2005).
[CrossRef] [PubMed]

Kiser, W. L.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging2(2), 113–123 (2003).
[CrossRef] [PubMed]

Klaase, J.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

Kolkman, R. G. M.

R. G. M. Kolkman, W. Steenbergen, and T. G. van Leeuwen, “In vivo photoacoustic imaging of blood vessels with a pulsed laser diode,” Lasers Med. Sci.21(3), 134–139 (2006).
[CrossRef] [PubMed]

Köster, R. W.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
[CrossRef]

Kruger, G. A.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging2(2), 113–123 (2003).
[CrossRef] [PubMed]

Kruger, R. A.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging2(2), 113–123 (2003).
[CrossRef] [PubMed]

Ku, G.

X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003).
[CrossRef] [PubMed]

Lacewell, R.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

Laufer, J.

J. Laufer, J. O. Cleary, E. Z. Zhang, M. F. Lythgoe, and P. C. Beard, “Photoacoustic imaging of vascular networks in transgenic mice,” Proc. SPIE7564, 75641A, 75641A-5 (2010).
[CrossRef]

Leonard, M. H.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

Lubatschowski, H.

U. Oberheide, I. Bruder, H. Welling, W. Ertmer, and H. Lubatschowski, “Optoacoustic imaging for optimization of laser cyclophotocoagulation,” J. Biomed. Opt.8(2), 281–287 (2003).
[CrossRef] [PubMed]

Lythgoe, M. F.

J. Laufer, J. O. Cleary, E. Z. Zhang, M. F. Lythgoe, and P. C. Beard, “Photoacoustic imaging of vascular networks in transgenic mice,” Proc. SPIE7564, 75641A, 75641A-5 (2010).
[CrossRef]

Ma, R.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
[CrossRef]

R. Ma, A. Taruttis, V. Ntziachristos, and D. Razansky, “Multispectral optoacoustic tomography (MSOT) scanner for whole-body small animal imaging,” Opt. Express17(24), 21414–21426 (2009).
[CrossRef] [PubMed]

Manohar, S.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

S. Manohar, A. Kharine, J. C. van Hespen, W. Steenbergen, and T. G. van Leeuwen, “The Twente Photoacoustic Mammoscope: system overview and performance,” Phys. Med. Biol.50(11), 2543–2557 (2005).
[CrossRef] [PubMed]

Mehta, K.

M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
[CrossRef] [PubMed]

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

Miller, K. D.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging2(2), 113–123 (2003).
[CrossRef] [PubMed]

Miller, T.

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

Ntziachristos, V.

A. Rosenthal, V. Ntziachristos, and D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys.38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

R. Ma, A. Taruttis, V. Ntziachristos, and D. Razansky, “Multispectral optoacoustic tomography (MSOT) scanner for whole-body small animal imaging,” Opt. Express17(24), 21414–21426 (2009).
[CrossRef] [PubMed]

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
[CrossRef]

Oberheide, U.

U. Oberheide, I. Bruder, H. Welling, W. Ertmer, and H. Lubatschowski, “Optoacoustic imaging for optimization of laser cyclophotocoagulation,” J. Biomed. Opt.8(2), 281–287 (2003).
[CrossRef] [PubMed]

Oraevsky, A.

A. Oraevsky and A. Karabutov, “Ultimate sensitivity of time-resolved opto-acoustic detection,” Proc. SPIE3916, 228–239 (2000).
[CrossRef]

Oraevsky, A. A.

M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
[CrossRef] [PubMed]

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

Paltauf, G.

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Probl.23(6), S65–S80 (2007).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography using integrating detectors,” Proc. SPIE5864, 586403, 586403-12 (2005).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl.20(5), 1663–1673 (2004).
[CrossRef]

Pang, Y. J.

X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003).
[CrossRef] [PubMed]

Perrimon, N.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
[CrossRef]

Piras, D.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

Razansky, D.

A. Rosenthal, V. Ntziachristos, and D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys.38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

R. Ma, A. Taruttis, V. Ntziachristos, and D. Razansky, “Multispectral optoacoustic tomography (MSOT) scanner for whole-body small animal imaging,” Opt. Express17(24), 21414–21426 (2009).
[CrossRef] [PubMed]

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
[CrossRef]

Reinecke, D. R.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging2(2), 113–123 (2003).
[CrossRef] [PubMed]

Rosenthal, A.

A. Rosenthal, V. Ntziachristos, and D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys.38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

Scherzer, O.

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography using integrating detectors,” Proc. SPIE5864, 586403, 586403-12 (2005).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl.20(5), 1663–1673 (2004).
[CrossRef]

Steenbergen, W.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

R. G. M. Kolkman, W. Steenbergen, and T. G. van Leeuwen, “In vivo photoacoustic imaging of blood vessels with a pulsed laser diode,” Lasers Med. Sci.21(3), 134–139 (2006).
[CrossRef] [PubMed]

S. Manohar, A. Kharine, J. C. van Hespen, W. Steenbergen, and T. G. van Leeuwen, “The Twente Photoacoustic Mammoscope: system overview and performance,” Phys. Med. Biol.50(11), 2543–2557 (2005).
[CrossRef] [PubMed]

Stoica, G.

X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003).
[CrossRef] [PubMed]

Su, R.

M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
[CrossRef] [PubMed]

Taruttis, A.

Ten Tije, E.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

van den Engh, F.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

van Hespen, J.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

van Hespen, J. C.

S. Manohar, A. Kharine, J. C. van Hespen, W. Steenbergen, and T. G. van Leeuwen, “The Twente Photoacoustic Mammoscope: system overview and performance,” Phys. Med. Biol.50(11), 2543–2557 (2005).
[CrossRef] [PubMed]

van Leeuwen, T.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

van Leeuwen, T. G.

R. G. M. Kolkman, W. Steenbergen, and T. G. van Leeuwen, “In vivo photoacoustic imaging of blood vessels with a pulsed laser diode,” Lasers Med. Sci.21(3), 134–139 (2006).
[CrossRef] [PubMed]

S. Manohar, A. Kharine, J. C. van Hespen, W. Steenbergen, and T. G. van Leeuwen, “The Twente Photoacoustic Mammoscope: system overview and performance,” Phys. Med. Biol.50(11), 2543–2557 (2005).
[CrossRef] [PubMed]

Vinegoni, C.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
[CrossRef]

Wang, L. V.

Z. Xu, Q. Zhu, and L. V. Wang, “In vivo photoacoustic tomography of mouse cerebral edema induced by cold injury,” J. Biomed. Opt.16(6), 066020 (2011).
[CrossRef] [PubMed]

M. H. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum.77(4), 041101 (2006).
[CrossRef]

X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003).
[CrossRef] [PubMed]

M. H. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056605 (2003).
[CrossRef] [PubMed]

Wang, X. D.

X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003).
[CrossRef] [PubMed]

Welling, H.

U. Oberheide, I. Bruder, H. Welling, W. Ertmer, and H. Lubatschowski, “Optoacoustic imaging for optimization of laser cyclophotocoagulation,” J. Biomed. Opt.8(2), 281–287 (2003).
[CrossRef] [PubMed]

Xia, W. F.

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

Xiang, D.

D. Xiang, N. N. Hsu, and G. V. Blessing, “The design, construction and application of a large aperture lens-less line-focus PVDF transducer,” Ultrasonics34(6), 641–647 (1996).
[CrossRef]

Xie, X. Y.

X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003).
[CrossRef] [PubMed]

Xu, M. H.

M. H. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum.77(4), 041101 (2006).
[CrossRef]

M. H. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056605 (2003).
[CrossRef] [PubMed]

Xu, Z.

Z. Xu, Q. Zhu, and L. V. Wang, “In vivo photoacoustic tomography of mouse cerebral edema induced by cold injury,” J. Biomed. Opt.16(6), 066020 (2011).
[CrossRef] [PubMed]

Zangerl, G.

M. Haltmeier and G. Zangerl, “Spatial resolution in photoacoustic tomography: effects of detector size and detector bandwidth,” Inverse Probl.26(12), 125002 (2010).
[CrossRef]

Zhang, E. Z.

J. Laufer, J. O. Cleary, E. Z. Zhang, M. F. Lythgoe, and P. C. Beard, “Photoacoustic imaging of vascular networks in transgenic mice,” Proc. SPIE7564, 75641A, 75641A-5 (2010).
[CrossRef]

Zhu, Q.

Z. Xu, Q. Zhu, and L. V. Wang, “In vivo photoacoustic tomography of mouse cerebral edema induced by cold injury,” J. Biomed. Opt.16(6), 066020 (2011).
[CrossRef] [PubMed]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control52(9), 1577–1583 (2005).
[CrossRef] [PubMed]

Inverse Probl.

P. Burgholzer, J. Bauer-Marschallinger, H. Grün, M. Haltmeier, and G. Paltauf, “Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors,” Inverse Probl.23(6), S65–S80 (2007).
[CrossRef]

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltauf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl.20(5), 1663–1673 (2004).
[CrossRef]

M. Haltmeier and G. Zangerl, “Spatial resolution in photoacoustic tomography: effects of detector size and detector bandwidth,” Inverse Probl.26(12), 125002 (2010).
[CrossRef]

J. Biomed. Opt.

Z. Xu, Q. Zhu, and L. V. Wang, “In vivo photoacoustic tomography of mouse cerebral edema induced by cold injury,” J. Biomed. Opt.16(6), 066020 (2011).
[CrossRef] [PubMed]

M. P. Fronheiser, S. A. Ermilov, H. P. Brecht, A. Conjusteau, R. Su, K. Mehta, and A. A. Oraevsky, “Real-time optoacoustic monitoring and three-dimensional mapping of a human arm vasculature,” J. Biomed. Opt.15(2), 021305 (2010).
[CrossRef] [PubMed]

S. A. Ermilov, T. Khamapirad, A. Conjusteau, M. H. Leonard, R. Lacewell, K. Mehta, T. Miller, and A. A. Oraevsky, “Laser optoacoustic imaging system for detection of breast cancer,” J. Biomed. Opt.14(2), 024007 (2009).
[CrossRef] [PubMed]

U. Oberheide, I. Bruder, H. Welling, W. Ertmer, and H. Lubatschowski, “Optoacoustic imaging for optimization of laser cyclophotocoagulation,” J. Biomed. Opt.8(2), 281–287 (2003).
[CrossRef] [PubMed]

Lasers Med. Sci.

R. G. M. Kolkman, W. Steenbergen, and T. G. van Leeuwen, “In vivo photoacoustic imaging of blood vessels with a pulsed laser diode,” Lasers Med. Sci.21(3), 134–139 (2006).
[CrossRef] [PubMed]

Med. Phys.

A. Rosenthal, V. Ntziachristos, and D. Razansky, “Model-based optoacoustic inversion with arbitrary-shape detectors,” Med. Phys.38(7), 4285–4295 (2011).
[CrossRef] [PubMed]

Mol. Imaging

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging2(2), 113–123 (2003).
[CrossRef] [PubMed]

Nat. Biotechnol.

X. D. Wang, Y. J. Pang, G. Ku, X. Y. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol.21(7), 803–806 (2003).
[CrossRef] [PubMed]

Nat. Photonics

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009).
[CrossRef]

Opt. Express

Phys. Med. Biol.

S. Manohar, A. Kharine, J. C. van Hespen, W. Steenbergen, and T. G. van Leeuwen, “The Twente Photoacoustic Mammoscope: system overview and performance,” Phys. Med. Biol.50(11), 2543–2557 (2005).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

M. H. Xu and L. V. Wang, “Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.67(5), 056605 (2003).
[CrossRef] [PubMed]

Proc. SPIE

M. Heijblom, D. Piras, E. Ten Tije, W. F. Xia, J. van Hespen, J. Klaase, F. van den Engh, T. van Leeuwen, W. Steenbergen, and S. Manohar, “Breast imaging using the Twente Photoacoustic Mammoscope (PAM): new clinical measurements,” Proc. SPIE8087, 80870N, 80870N-7 (2011).
[CrossRef]

J. Laufer, J. O. Cleary, E. Z. Zhang, M. F. Lythgoe, and P. C. Beard, “Photoacoustic imaging of vascular networks in transgenic mice,” Proc. SPIE7564, 75641A, 75641A-5 (2010).
[CrossRef]

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography using integrating detectors,” Proc. SPIE5864, 586403, 586403-12 (2005).
[CrossRef]

A. Oraevsky and A. Karabutov, “Ultimate sensitivity of time-resolved opto-acoustic detection,” Proc. SPIE3916, 228–239 (2000).
[CrossRef]

Rev. Sci. Instrum.

M. H. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum.77(4), 041101 (2006).
[CrossRef]

Ultrasonics

D. Xiang, N. N. Hsu, and G. V. Blessing, “The design, construction and application of a large aperture lens-less line-focus PVDF transducer,” Ultrasonics34(6), 641–647 (1996).
[CrossRef]

Other

G. Paltauf, R. Nuster, M. Haltmeier, and P. Burgholzer, “Photoacoustic tomography with integrating area and line detectors,” in Photoacoustic Imaging and Spectroscopy, L. V. Wang, ed. (CRC Press, Boca Raton, FL, 2009), pp. 251–263.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) Schematic drawing of a cylindrical detector and the focusing area from a side view; (b) drawing illustrating the relation between radius R of the detector, radius b of the object and length L of the detector.

Fig. 2
Fig. 2

Simulated image of a phantom consisting of five homogenously heated spheres. (a) Reconstruction from pressure signals acquired over 360°, (b) reconstruction from Abel transformed pressure signals acquired over 360°, (c) pressure signals over 180°, (d) Abel transformed signals over 180°.

Fig. 3
Fig. 3

Experimental setup seen from above: l1 and l2 are cylindrical lenses focusing onto one plane of the phantom (ph), as indicated by the green line in Fig. 1(a).

Fig. 4
Fig. 4

(a) Reconstructed image of a single sphere in a plane parallel to the rotation axis; (b) profile of a single sphere in z-direction.

Fig. 5
Fig. 5

(a) Section image of a single black hair with a diameter of 80 µm; (b) profile in x-direction.

Fig. 6
Fig. 6

(a) photograph of the embedded zebrafish; (b)–(g) sections of the zebrafish (indicated as green lines in (a)): sc, spinal cord; pf, pelvic fins; vf, ventral fins; e, eyes.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

NA= a 2R
L=4 b 2 +bR
M[ p 0 2D ]( u 0 , v 0 ,r)=4r c s 0 r/ c s p 2D ( u 0 , v 0 ,t) r 2 c s 2 t 2 dt.

Metrics